algoadvance

You are given a string of length 5 that represents the time in the format "HH:MM". The string can contain digits and/or the character '?' which can represent any digit from 0 to 9. You need to return the total number of valid times the string can represent.

A valid time is in the range from "00:00" to "23:59".

Clarifying Questions

1. Input Constraints: What are the constraints on the input? For example, are there any cases where "?" will appear outside the HH:MM format?
   • Clarification: The string will always be in the format "HH:MM" and will always be of length 5. The ? will only appear in place of digits.
2. Edge Cases: Can the input string contain entirely wildcards such as "??:??"?
   • Clarification: Yes, the input can contain up to 5 wildcards.
3. Output: What are we supposed to return?
   • Clarification: Return an integer representing the number of valid times.

Strategy

1. Iterate Through Possible Values for Each Character:
   • We will iterate through all possible hours and minutes.
   • Check if the current time matches the given format including wildcards.
   • Count the matches that represent valid times.
2. Validation:
   • For each possible time, convert hour and minute to strings with zero-padding.
   • Check if they match the pattern provided.

Code

def countTime(time: str) -> int:
    count = 0
    
    for hour in range(24):
        for minute in range(60):
            hh = f'{hour:02d}'
            mm = f'{minute:02d}'
            valid = True
            
            for i in range(2):
                if time[i] != '?' and time[i] != hh[i]:
                    valid = False
                    break
            
            for i in range(3, 5):
                if time[i] != '?' and time[i] != mm[i - 3]:
                    valid = False
                    break
            
            if valid:
                count += 1
    
    return count

# Example usage:
time = "1?:45"
print(countTime(time))  # Output would depend on the example

Time Complexity

• Nested Loops: O(24 * 60)
  • Outer loop iterates over hours (0-23): 24 iterations.
  • Inner loop iterates over minutes (0-59): 60 iterations.
• String Comparison: O(1)
  • Each check involves fixed-length string comparison operations.
• Overall: The overall time complexity is O(24 * 60) = O(1440), which is effectively constant time (O(1)) in practical scenarios given the fixed upper limits.

We iterate efficiently checking each specific valid time and determine if they align with the provided pattern.

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